ASCE STANDARD

ASCE/SEI

4-16

Seismic Analysis of Safety-Related Nuclear Structures

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ASCE STANDARD ASCE/SEI

4-16

Seismic Analysis ofSafety-Related NuclearStructures

PUBLISHED BY THE AMERICAN SOCIETY OF CIVIL ENGINEERS

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Library of Congress Cataloging-in-Publication Data

Names: American Society of Civil Engineers.Title: Seismic analysis of safety-related nuclear structures / American Society of CivilEngineers.Description: Reston, Virginia : American Society of Civil Engineers, 2017. | “ASCE standardASCE/SEI 4-16.” | Includes bibliographical references and index.Identifiers: LCCN 2016045567 (print) | LCCN 2016056049 (ebook) | ISBN9780784413937 (pbk. : alk. paper) | ISBN 9780784479988 (PDF)Subjects: LCSH: Nuclear facilities–Evaluation–Standards–United States. | Earthquakeresistant design–Standards–United States. | Nuclear facilities–Earthquake effects.Classification: LCC TK9152.163 .A47 2017 (print) | LCC TK9152.163 (ebook) | DDC621.48/35–dc23LC record available at https://lccn.loc.gov/2016045567

Published by American Society of Civil Engineers1801 Alexander Bell DriveReston, Virginia, 20191-4382www.asce.org/bookstore | ascelibrary.org

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Errata: Errata, if any, can be found at https://doi.org/10.1061/9780784413937.

Copyright © 2017 by the American Society of Civil Engineers.All Rights Reserved.ISBN 978-0-7844-1393-7 (print)ISBN 978-0-7844-7998-8 (PDF)Manufactured in the United States of America.

22 21 20 19 18 17 1 2 3 4 5

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ASCE STANDARDS

In 2014, the Board of Direction approved revisions to the ASCERules for Standards Committees to govern the writing andmaintenance of standards developed by ASCE. All such stan-dards are developed by a consensus standards process managedby the ASCE Codes and Standards Committee (CSC). Theconsensus process includes balloting by a balanced standardscommittee and reviewing during a public comment period. Allstandards are updated or reaffirmed by the same process everyfive to 10 years. Requests for formal interpretations shall beprocessed in accordance with Section 7 of ASCE Rules forStandards Committees, which are available at www.asce.org.Errata, addenda, supplements, and interpretations, if any, for thisstandard can also be found at www.asce.org.

This standard has been prepared in accordance with recog-nized engineering principles and should not be used withoutthe user’s competent knowledge for a given application. Thepublication of this standard by ASCE is not intended to warrantthat the information contained herein is suitable for any generalor specific use, and ASCE takes no position respecting thevalidity of patent rights. The user is advised that the determi-nation of patent rights or risk of infringement is entirely theirown responsibility.

A complete list of currently available standards is availablein the ASCE Library (http://ascelibrary.org/page/books/s-standards).

iii

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DEDICATION

John D. Stevenson, Ph.D., P.E.May 23, 1933–October 30, 2014

ASCE 4-16 is dedicated to Dr. John D. Stevenson: a leader in the nuclear energyindustry for more than four decades, with seminal contributions in civil, structural, andmechanical engineering.John Stevenson graduated with a bachelor of science degree from Virginia Military

Institute (VMI) in 1954. After two years of service in the U.S. Army Corps of Engineersand six years of service on the faculty of VMI, he completed a master of science degreeat Case Institute of Technology in 1962. Two years of research on nuclear weaponseffects at the IIT Research Institute in Chicago followed, after which he began doctoralstudies at Case Western University. He completed his Ph.D. at Case Western in 1968.Between 1968 and 1981, John held senior positions with Westinghouse Electric

Company, Case Western Reserve University, McKee and Company, and WoodwardClyde Consultants. In 1981, he founded Stevenson and Associates, a consultingengineering firm, which grew rapidly and had offices in Cleveland, Ohio; Boston,Massachusetts; Pilsen, Czech Republic; St. Petersburg, Russia; and Bucharest, Roma-nia. He also served as a consulting engineer to the U.S. Nuclear Regulatory Commis-sion, the Defense Nuclear Facility Safety Board, and the International Atomic EnergyAgency.John received many awards over his career, including the American Society of Civil

Engineers (ASCE) Mosieff Award in 1971, the Civil Engineer of the Year in 1991 givenby the Cleveland Section of the ASCE, the ASCE Stephen Bechtel Award in 1995, andthe American Society of Mechanical Engineers (ASME) Bernard Langer Award in1997.A hallmark of John’s career in the nuclear industry, which spanned more than 40

years, is his many important contributions to codes and standards for safety-relatednuclear structures published by the American Concrete Institute, American Institute ofSteel Construction, American Nuclear Society, American Society of Civil Engineers,and American Society of Mechanical Engineers: a broad spectrum of importantcontributions that collectively are likely unmatched in the nuclear industry in theUnited States.John was an active member of the ASCE Committee on Dynamic Analysis of Nuclear

Structures. He brought much to the committee, including a deep understanding ofmechanical components and systems and ASME codes and standards. Frequently, hewas the lone advocate for mechanical engineering systems in a roomful of civil andstructural engineers. His efforts to extend ASCE Standards 4 and 43 to addressmechanical components and systems greatly expanded the utility of these standards,which will be forever appreciated.Through this dedication, the members of the ASCE 4 task committee acknowledge

John’s seminal contributions to the seismic engineering of safety-related nuclearstructures. His absence from committee deliberations and vigorous discussions is, andwill be, sadly missed.

Seismic Analysis of Safety-Related Nuclear Structures v

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CONTENTS

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

ABBREVIATIONS AND NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix

1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2.1 Types of Structures Covered by This Standard . . . . . . . . . . . . . . . . . . . . . . 11.1.2.2 Foundation Material Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.3 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.1 Use of Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.2 Use of ASCE 4 with Other Codes and Standards . . . . . . . . . . . . . . . . . . . . 11.1.3.3 Alternative Methodologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Seismic Quality Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Analysis Verification and Documentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Load Path Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.3 Independent Peer Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1A Attachment: On Achieving Target Performance Goals (Nonmandatory). . . . . . . . . . . . . . . . . . . . 21A.1 Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21A.2 Expected Factors of Safety Achieved by Seismic Acceptance Criteria . . . . . . . . . . . . . . . . . . . . 2

1A.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21A.2.2 Estimation of Median Conservatism Introduced by Standard Seismic Acceptance Criteria . . . . . 3

1A.2.2.1 Median Strength Conservatism Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 31A.2.2.2 Median Demand Conservatism Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 31A.2.2.3 Median Nonlinear Conservatism Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 31A.2.2.4 Resulting Capacity Conservatism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

References for Attachment 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 SEISMIC INPUT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Performance-Based Design Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Input Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Input Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Soil Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Probabilistic Site Response Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.1 Soil Profile Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.2 Analysis Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.2.1 Development of Low-Strain Realizations . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.2.2 Ground Response Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Strain-Compatible Soil Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Design Response Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.5.1 Target Response Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.5.2 Types of Design Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.5.3 Vertical Design Response Spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.6 Design Response Spectrum–Compatible Ground Motion Histories . . . . . . . . . . . . . . . . . . . . . . 62.6.1 Requirements for DRS-Compatible Ground Motion Histories . . . . . . . . . . . . . . . . . . . . 62.6.2 Ground Motion History Development Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7 Structures Sensitive to Low-Frequency Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.7.1 Response Spectra Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

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2.7.2 Ground Motion Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.8 Alternative Definitions of Design Ground Motions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 MODELING OF STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Models for Horizontal and Vertical Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 Multistep and One-Step Methods of Seismic Response Analysis . . . . . . . . . . . . . . . . . . 9

3.1.2.1 Models for Multistep Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2.2 Models for One-Step Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.3 Discretization Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1.3.1 Selection of Finite Element Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1.3.2 Selection of Mesh Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1.3.3 Stick Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.4 Alternate Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Structural Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2.1 Modulus of Elasticity and Poisson’s Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.1.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.1.2 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2.2 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 Modeling of Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.2 Stiffness of Reinforced Concrete Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4 Modeling of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4.1 Discretization of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4.2 Determination of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.5 Modeling of Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5.1 Damping Properties of Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.5.1.1 Proportional Damping (Rayleigh Damping) . . . . . . . . . . . . . . . . . . . . . . . 123.5.1.2 Complex Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.5.2 Composite Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5.2.1 Substructures with Different Damping Ratios . . . . . . . . . . . . . . . . . . . . . . 123.5.2.2 Substructures with Proportional Damping. . . . . . . . . . . . . . . . . . . . . . . . . 12

3.5.3 Composite Modal Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5.4 Alternate Composite Modal Damping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.6 Modeling of Hydrodynamic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.6.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.6.2 Dynamic Analysis Formulation for Submerged Structures . . . . . . . . . . . . . . . . . . . . . . 133.6.3 Hydrodynamic Mass Effects on Building Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.7 Dynamic Coupling Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.7.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.7.2 Single-Point Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.7.3 Multipoint Attachment and Static Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.8 Additional Requirements for Modeling Specific Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 143.8.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.8.1.1 Structures with Rigid Floor Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . 143.8.1.2 Structures with Flexible Floor Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . 153.8.1.3 Requirements for Lumped-Mass Stick Models . . . . . . . . . . . . . . . . . . . . . . 15

3.8.2 Requirements for Frame Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.8.3 Requirements for Shear Wall Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.8.4 Requirements for Plate and Shell Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.8.5 Requirements for Adjacent Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 ANALYSIS OF STRUCTURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2 Linear Response-History Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2.2 Combination of Spatial Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2.3 Systems with Multiple Supports. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Linear Response-Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.2 Combination of Modal Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.3 Combination of Spatial Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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4.3.4 Combination of Multiple Response Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3.5 Systems with Multiple Supports. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.4 Frequency-Domain Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.5 Equivalent Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.5.1 Application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.5.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.6 Multistep Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.6.1 Initial Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.6.2 Subsequent Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.6.3 Subsequent Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.6.3.1 Response-Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.6.3.2 Response-History Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.6.4 Limitations of the Multistep Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.7 Nonlinear Response-History Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.7.2 Mathematical Models of Components and Elements . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.7.2.1 Structural Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.7.2.2 Models of Nonstructural Components. . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.7.3 Sets of Ground Motions for Response Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.8 Approximate Inelastic Response-Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.9 Nonlinear Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.9.2 Mathematical Models of Components and Elements . . . . . . . . . . . . . . . . . . . . . . . . . 224.9.3 Calculation of Target Displacement for Response Analysis . . . . . . . . . . . . . . . . . . . . . 22

5 SOIL-STRUCTURE INTERACTION MODELING AND ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . 235.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.1.1 Fixed-Base Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.1.2 Spatial Variations of Free-Field Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.1.3 Three-Dimensional Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.1.4 Nonlinear Behavior of Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.1.5 Structure-Soil-Structure Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1.6 Effect of Mat and Lateral Wall Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1.7 Uncertainties in SSI Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1.8 Model of Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1.9 Embedment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.10 Wave Incoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.11 Validation of SSI Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2 Subsurface Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.3 Direct Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.3.1 Seismic Input for Model Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3.2 Lower Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3.3 Selection of Lateral Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3.4 Soil Element Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3.5 Time Step and Frequency Increment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.4 Substructuring Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.4.1 Determination of Input Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.4.1.1 SSI Input Motion Consistent with SSI Modeling. . . . . . . . . . . . . . . . . . . . . 265.4.1.2 Recorded Earthquake Ground Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . 275.4.1.3 Foundation Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.4.2 Determination of Foundation-Impedance Functions . . . . . . . . . . . . . . . . . . . . . . . . . 275.4.2.1 Foundation Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.4.2.2 Uniform Soil Sites: Simplified Soil Spring Method . . . . . . . . . . . . . . . . . . . 275.4.2.3 Layered Soil Sites: Simplified Soil Spring Method. . . . . . . . . . . . . . . . . . . . 275.4.2.4 Embedded Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.4.3 Analysis of Coupled Soil-Structural System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4.4 Frequency Cutoff and Frequency Increment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.5 Probabilistic SSI Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.5.1 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.5.2 Variability of Structural Stiffness and Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.5.3 Variability of Soil Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.5.4 Input Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.5.4.1 Input Motion Defined as Time Series Sets . . . . . . . . . . . . . . . . . . . . . . . . 29

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5.5.4.2 Input Motion Defined as Acceleration Response Spectra . . . . . . . . . . . . . . . . 295.5.5 Response Analysis Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.5.5.1 Monte Carlo Simulation (MCS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.5.5.2 Latin Hypercube Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6 INPUT FOR SUBSYSTEM ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1.1 Types of Seismic Input for Subsystem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.1.2 Directions and Locations for In-Structure Response Spectra and/or Time Series . . . . . . . . . . 316.1.3 Subsystem Input away from Reference Location . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.1.4 In-Structure Displacements and Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.1.5 Probabilistically Defined In-Structure Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.2 In-Structure Response Spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.2.1 Methods of Generating In-Structure Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . 32

6.2.1.1 Time Series Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.2.1.2 Direct Spectra-to-Spectra Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.2.1.3 Probabilistically Defined In-Structure Response Spectra . . . . . . . . . . . . . . . . . 32

6.2.2 Frequency Interval for Generation of In-Structure Response Spectra . . . . . . . . . . . . . . . . 326.2.3 Treatment of Uncertainties in Generating In-Structure Response Spectra . . . . . . . . . . . . . . 326.2.4 Interpolation of In-Structure Response Spectra for Intermediate Damping . . . . . . . . . . . . . 336.2.5 Effect of Seismic Wave Incoherence on In-Structure Response Spectra. . . . . . . . . . . . . . . 33

6.3 In-Structure Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.3.1 Methods for Generation of In-Structure Time Series . . . . . . . . . . . . . . . . . . . . . . . . . 336.3.2 Equivalent Broadening and Lowering of In-Structure Time Series . . . . . . . . . . . . . . . . . 336.3.3 Time Interval and Data Precision Requirements for In-Structure Time Series. . . . . . . . . . . . 346.3.4 Probabilistically Defined In-Structure Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . 34

6.4 Structural Model or Characteristics for Coupled Subsystem Analysis . . . . . . . . . . . . . . . . . . . . . 346.4.1 Supporting Soil-Structure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346.4.2 Base Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

6.5 Subsystem Damping Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

7 BURIED PIPES AND CONDUITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.1 Straight Sections Remote from Anchor Points, Sharp Bends, or Intersections . . . . . . . . . . . . . . . . 37

7.1.1 Maximum Axial Strain Ignoring Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.1.2 Maximum Axial Strain Considering Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.1.3 Maximum Curvature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.1.4 Maximum Joint Displacement and Rotation in Segmented Structures . . . . . . . . . . . . . . . . 37

7.2 Forces on Bends, Intersections, and Anchor Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.3 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.4 Anchor Point Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

8 DYNAMIC SOIL PRESSURES ON WALLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398.2 Embedded Building Walls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

8.2.1 Dynamic Finite Element Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398.2.2 Simplified Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398.2.3 Alternate Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

8.3 Earth-Retaining Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

9 VERTICAL LIQUID-STORAGE TANKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.2 Horizontal Impulsive Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

9.2.1 Effective Weight of Liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.2.2 Spectral Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.2.3 Overturning Moment at Base of Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.2.4 Overturning Moment below Base of Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.2.5 Hydrodynamic Pressure on Tank Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

9.3 Horizontal Sloshing Mode (Convective Mode) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.3.1 Effective Weight of Liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.3.2 Spectral Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

x ASCE/SEI STANDARD 4-16

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9.3.3 Overturning Moment at Base of Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.3.4 Overturning Moment below Base of Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.3.5 Hydrodynamic Pressure on Tank Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.3.6 Liquid Slosh Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

9.4 Vertical Liquid Response Mode Hydrodynamic Pressure on Tank Shell . . . . . . . . . . . . . . . . . . . 429.5 Other Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

9.5.1 Overturning Moment and Longitudinal Compressive Force . . . . . . . . . . . . . . . . . . . . . 429.5.2 Dynamic Pressure and Maximum Stresses in Tank Shell . . . . . . . . . . . . . . . . . . . . . . 429.5.3 Freeboard Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429.5.4 Special Provisions for Nearly Full Tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429.5.5 Attached Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429.5.6 Tank Foundation and Anchorage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

10 DISTRIBUTION SYSTEMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4310.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4310.2 Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

10.2.1 Elevated Temperature Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4310.2.2 Cold Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4410.2.3 Piping Deadweight Support Spacing and Fundamental Frequencies as a Function of Support

Spacing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4410.3 Pipe Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510.4 Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510.5 Ductwork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510.6 Raceways. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

10.6.1 Seismic Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4610.6.2 Transverse Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

10.6.2.1 Unbraced System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4610.6.2.2 Braced System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

10.6.3 Longitudinal Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710.6.3.1 Unbraced System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710.6.3.2 Braced System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

10.6.4 Vertical Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810.7 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810.8 Combination of Spatial Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810A Attachment: Simplified Design of Cold Piping by the Load Coefficient Method and Design by Rule

(Nonmandatory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810A.2 Load Coefficient Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

10A.2.1 Proportioning of Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810A.2.2 Application of Seismic Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

10A.3 Design by Rule Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4810A.4 Cold Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4910A.5 Application of the Seismic Load Coefficient and Design by Rule Methods. . . . . . . . . . . . . . . . . . 49

10A.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4910A.5.2 Application of the Load Coefficient Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4910A.5.3 Typical Earthquake In-Structure Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 4910A.5.4 Application of Design by Rule and Load Coefficient Method . . . . . . . . . . . . . . . . . . . . 51

10A.6 Procedure for Determining Design by Rule Spectral Acceleration Limits for LVSSR of 1 to 4 . . . . . . . 5110A.6.1 Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

10A.6.1.1 Sample Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5110A.6.1.2 Application of Seismic Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5210A.6.1.3 Evaluation of Seismic Anchor Motion Stresses. . . . . . . . . . . . . . . . . . . . . . 52

10A.6.2 Application of the Equivalent Static Analysis of a Peak Spectral Acceleration of Figure 10A-2with a Bump Factor of 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

10A.6.3 Result of LCM Applied to Design by Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52References for Attachment 10A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

11 DYNAMIC SLIDING AND UPLIFT ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5511.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5511.2 Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

11.2.1 Simplified Nonlinear Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5511.2.2 Nonlinear Response-History Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5511.2.3 Consideration of Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Seismic Analysis of Safety-Related Nuclear Structures xi

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11.3 Acceptable Approximate Methods for Analysis of Sliding and Rocking of an Unanchored Rigid Body . . 5611.3.1 Approximate Method for Analysis of Sliding of an Unanchored Rigid Body. . . . . . . . . . . . 5611.3.2 Approximate Method for Computing Rocking of an Unanchored Rigid Body . . . . . . . . . . . 56

11A Attachment: Comments on Analysis and Design of Anchorage for Structures and Components(Nonmandatory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

11A.1 Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5711A.2 Determining the Potential for Overturning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5811A.3 Anchorage of Electrical and Mechanical Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

References for Attachment 11A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

12 SEISMICALLY ISOLATED STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.2 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

12.2.1 Isolation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.2.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.2.1.2 Vertical Load Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.2.1.3 Minimum Lateral Restoring Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.2.1.4 Wind Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6112.2.1.5 Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6212.2.1.6 Inspection and Replacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

12.2.2 Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6212.2.2.1 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6212.2.2.2 Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

12.2.3 Basemat and Foundation Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6212.3 Seismic Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6312.4 Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

12.4.1 Methods of Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6312.4.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6312.4.1.2 Time-Domain Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6312.4.1.3 Frequency-Domain Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6312.4.1.4 Multistep Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

12.4.2 Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6412.4.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6412.4.2.2 Mathematical Models of Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6412.4.2.3 Equivalent Linear Models of Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . 6412.4.2.4 Nonlinear Models of Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

12.5 Displacements and Forces for Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6412.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6412.5.2 Seismic Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.5.3 Stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.5.4 Structures, Systems, and Components above the Isolation Interface . . . . . . . . . . . . . . . . . 6512.5.5 Structure below the Isolation Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.5.6 Systems and Components Crossing the Isolation Interface. . . . . . . . . . . . . . . . . . . . . . 65

12.6 Peer Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.7 Testing of Prototype and Production Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

12.7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.7.2 Prototype Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

12.7.2.1 Test Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.7.2.2 Record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.7.2.3 Sequence and Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6512.7.2.4 Test Specimen Adequacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

12.7.3 Production Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6612.7.3.1 Test Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6612.7.3.2 Record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6612.7.3.3 Sequence and Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6612.7.3.4 Test Specimen Adequacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

APPENDIX A: PROCEDURES TO IDENTIFY PLANT-LEVEL SEISMIC VULNERABILITIES AND RISK(NONMANDATORY) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67A.2 Purpose and Overview of Seismic Probabilistic Risk Assessment . . . . . . . . . . . . . . . . . . . . . . . 68A.3 Purpose and Overview of Seismic Margin Assessment Methodology . . . . . . . . . . . . . . . . . . . . . 70

xii ASCE/SEI STANDARD 4-16

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A.4 Comparison of Seismic Evaluation Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

APPENDIX B: NONLINEAR TIME-DOMAIN SOIL-STRUCTURE INTERACTION (NONMANDATORY) . . . . . . 75B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75B.2 Development of Finite Element Meshes for Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75B.3 Ground Motion Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76B.4 Nonlinear Constitutive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76B.5 Analysis Results and Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77B.6 Verification and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

COMMENTARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

C1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81C1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81C1.2 Seismic Quality Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

C2 SEISMIC INPUT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83C2.1 Performance-Based Design Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83C2.2 Input Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C2.2.2 Soil Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84C2.3 Probabilistic Site Response Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C2.3.1 Soil Profile Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84C2.3.2 Analysis Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C2.3.2.1 Development of Low-Strain Realizations . . . . . . . . . . . . . . . . . . . . . . . . . 84C2.3.2.2 Ground Response Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C2.5 Design Response Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86C2.5.1 Target Response Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86C2.5.2 Types of Design Response Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86C2.5.3 Vertical Design Response Spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

C2.6 Design Response Spectrum–Compatible Ground Motion Histories . . . . . . . . . . . . . . . . . . . . . . 87C2.6.1 Requirements for DRS-Compatible Ground Motion Histories . . . . . . . . . . . . . . . . . . . . 87C2.6.2 Ground Motion History Development Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 87

C2.8 Alternative Definitions of Design Ground Motions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

C3 MODELING OF STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89C3.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

C3.1.1 Models for Horizontal and Vertical Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90C3.1.2 Multistep and One-Step Methods of Seismic Response Analysis . . . . . . . . . . . . . . . . . . 90C3.1.3 Discretization Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

C3.1.3.1 Selection of Finite Element Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90C3.1.3.2 Selection of Mesh Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

C3.1.4 Alternate Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C3.2 Structural Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

C3.2.1 Modulus of Elasticity and Poisson’s Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C3.2.1.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C3.2.1.2 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

C3.2.2 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C3.3 Modeling of Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

C3.3.1 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C3.3.2 Stiffness of Reinforced Concrete Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

C3.4 Modeling of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93C3.4.1 Discretization of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93C3.4.2 Determination of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

C3.5 Modeling of Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93C3.5.1 Damping Properties of Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Seismic Analysis of Safety-Related Nuclear Structures xiii

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